The present invention relates to a method and an apparatus for displaying a geometric form characteristic, and more particularly to a method of displaying a form for use in a form designing/machining analyzing/visualizing system incorporating a computer, for example, mechanical CAD (Computer Aided Design)/CAM (Computer Aided Manufacturing)/CAE (Computer Aided Engineering), and CG (Computer Graphics).
When the form of an industrial product or the like is designed by using a form design aiding system such as a mechanical CAD, the form is usually expressed by using a geometric model in the computer. However, the geometric model designed in the computer does not necessarily meet the form imagined by the user. The reasons for this are that the form expressing method in the computer is based on the geometric model and, accordingly, the form expressing command function of the computer is unsatisfactory to express the form imagined by the user, and in particular, to express a free form surface as a geometric model and that performance is insufficient to display the three-dimensional geometric model constituted in the computer on a display device such as a CRT (Cathode Ray Tube).
As a means for overcoming the foregoing problems, it might be considered feasible to employ a method for actually making a model by a model making machine adapted to NC (Numerical Control) cutting work or a method for making a resin model by a perspective resin model making system which uses photosetting resin. In any case, a machining operation must be performed and the model cannot be made in real time. Therefore, the form cannot be modified while establishing a dialogue with the computer.
Another method can be employed capable of displaying a geometric model, designed in a computer, on a display device such as a CRT in a short time, while eliminating the necessity of machining the geometric model. A major portion of the foregoing methods is arranged to perform an optical simulation by using a computer to simulate how a three-dimensional form may appear under a certain light source.
Since the internal portion of a free form surface is expressed by a functional equation, a method may be employed in which a problem of a geometric model designed in a computer is found out by adding a geometric form characteristic, such as the distribution of a normal vector, a curvature vector, a Gaussian curvature, and the mean curvature to the form, followed by displaying them. For example, Japanese Patent Laid-Open No. 62-271067 titled "FREE FORM SURFACE EXPRESSING METHOD" discloses a method of displaying a normal vector at a boundary line between patches to check smoothness connected between a plurality of patches that constitute the free form surface. However, any of the foregoing method simply confirms whether or not the geometric form characteristics are distributed continuously, resulting in a form considerably different from that imagined by a user. Therefore, it is difficult to quickly modify the form by making use of the result of the display.
In Japanese Patent Laid-Open No. 3-278182 titled "METHOD AND APPARATUS FOR SENSITIVELY NOTIFYING FORM", the foregoing problem experienced with a geometric form characteristic expressed by three-dimensional vector such as a normal vector or a curvature vector has been partially overcome in terms of the machine interface by instructing a point on the form displayed on the screen by using a pointing device such as a mouse. However, the geometric form characteristic has not been displayed with which the user is able to easily understand the form.